Physics of band-gap formation and its evolution in the pillar-based phononic crystal structures

Abstract

In this paper, the interplay of Bragg scattering and local resonance is theoretically studied in a phononic crystal (PnC) structure composed of a silicon membrane with periodic tungsten pillars. The comparison of phononic band gaps (PnBGs) in three different lattice types (i.e., square, triangular, and honeycomb) with different pillar geometries shows that different PnBGs have varying degrees of dependency on the lattice symmetry based on the interplay of the local resonances and the Bragg effect. The details of this interplay is discussed. The significance of locally resonating pillars, specially in the case of tall pillars, on PnBGs is discussed and verified by examining the PnBG position and width in perturbed lattices via Monte Carlo simulations. It is shown that the PnBGs caused by the local resonance of the pillars are more resilient to the lattice perturbations than those caused by Bragg scattering.

Phonon and heat transport control using pillar-based phononic crystals

“…First, like in the hole-based PnCs [2], the periodicity of pillars creates Bragg diffraction of mechanical waves [27], similar to that of photons in photonic crystals [28,29]. For example, the first two branches in Figure 1 are flattened due to the periodicity of the pillars [30].…”

“…The flattening of the dispersion branches due to both Bragg diffraction and the local resonances can form phononic bandgaps—the ranges of frequency, in which phonons cannot propagate [27,35,36]. The frequency of the Bragg bandgap is linked to the period of the PnCs and thus affects only phonons with the wavelengths of about the characteristic size of the system [27,35,37].…”

“…The frequency of the Bragg bandgap is linked to the period of the PnCs and thus affects only phonons with the wavelengths of about the characteristic size of the system [27,35,37]. The frequencies of the local resonance bandgaps are linked to the resonant frequencies of the pillars [27], which can be tuned via structural parameters, such as pillar diameter [30,38] and height [25,26,30,38,39], or material parameters, such as density and Young modulus [25,30]. Thus, the local resonance bandgaps can be opened at higher [27] or lower [39,40] frequencies than the Bragg bandgap.…”

“…The frequencies of the local resonance bandgaps are linked to the resonant frequencies of the pillars [27], which can be tuned via structural parameters, such as pillar diameter [30,38] and height [25,26,30,38,39], or material parameters, such as density and Young modulus [25,30]. Thus, the local resonance bandgaps can be opened at higher [27] or lower [39,40] frequencies than the Bragg bandgap. Moreover, unlike Bragg bandgaps, the local resonance bandgaps are independent of the periodicity of pillars and are insensitive to the period disorder [27,39].…”

“…Thus, the local resonance bandgaps can be opened at higher [27] or lower [39,40] frequencies than the Bragg bandgap. Moreover, unlike Bragg bandgaps, the local resonance bandgaps are independent of the periodicity of pillars and are insensitive to the period disorder [27,39]. …”